Consequences of Weyl Consistency Conditions

The running of quantum field theories can be studied in detail with the use of a local renormalization group equation. The usual beta-function effects are easy to include, but by introducing spacetime-dependence of the various parameters of the theory one can efficiently incorporate renormalization effects of composite operators as well. An illustration of the power of these methods was presented by Osborn in the early 90s, who used consistency conditions following from the Abelian nature of the Weyl group to rederive Zamolodchikov's c-theorem in d=2 spacetime dimensions, and also to obtain a perturbative a-theorem in d=4. In this work we present an extension of Osborn's work to d=6 and to general even d. We compute the full set of Weyl consistency conditions, and we discover among them a candidate for an a-theorem in d=6, similar to the d=2,4 cases studied by Osborn. Additionally, we show that in any even spacetime dimension one finds a consistency condition that may serve as a generalization of the c-theorem, and that the associated candidate c-function involves the coefficient of the Euler term in the trace anomaly. Such a generalization hinges on proving the positivity of a certain "metric" in the space of couplings.Comment: 19 pages, Mathematica file with consistency conditions included in submission. v2: Fixed typo

A challenge to the aa-theorem in six dimensions

The possibility of a strong $a$-theorem in six dimensions is examined in multi-flavor $\phi^3$ theory. Contrary to the case in two and four dimensions, we find that in perturbation theory the relevant quantity $\tilde{a}$ increases monotonically along flows away from the trivial fixed point. $\tilde{a}$ is a natural extension of the coefficient $a$ of the Euler term in the trace anomaly, and it arises in any even spacetime dimension from an analysis based on Weyl consistency conditions. We also obtain the anomalous dimensions and beta functions of multi-flavor $\phi^3$ theory to two loops. Our results suggest that some new intuition about the $a$-theorem is in order.Comment: 4 pages. v2: Fixed typos, added reference

STUDIES IN MALESIAN PANDANACEAE VII. A REVIEW OF JAVANESE PANDANACEAE, WITH NOTES ON PLANTS CULTIVATED IN THE HORTUS BOGORIENSIS

In the light of recent monographic studies it has been found necessary to augment and revise to some extent the treatment of Javanese Pandanaceae in Backer & Bakhuizen van den Brink's "Flora of Java". Several name changes are suggested and some species omitted by these authors are enumerated. Notes on various species of different origin now cultivated in the Hortus Bogoriensis are also included. Pandanus sect. Multispina Fagerlind is reduced to a subsection of Pandanus sect. Rykia

A Design Thinking Framework for Human-Centric Explainable Artificial Intelligence in Time-Critical Systems

Artificial Intelligence (AI) has seen a surge in popularity as increased computing power has made it more viable and useful. The increasing complexity of AI, however, leads to can lead to difficulty in understanding or interpreting the results of AI procedures, which can then lead to incorrect predictions, classifications, or analysis of outcomes. The result of these problems can be over-reliance on AI, under-reliance on AI, or simply confusion as to what the results mean. Additionally, the complexity of AI models can obscure the algorithmic, data and design biases to which all models are subject, which may exacerbate negative outcomes, particularly with respect to minority populations. Explainable AI (XAI) aims to mitigate these problems by providing information on the intent, performance, and reasoning process of the AI. Where time or cognitive resources are limited, the burden of additional information can negatively impact performance. Ensuring XAI information is intuitive and relevant allows the user to quickly calibrate their trust in the AI, in turn improving trust in suggested task alternatives, reducing workload and improving task performance. This study details a structured approach to the development of XAI in time-critical systems based on a design thinking framework that preserves the agile, fast-iterative approach characteristic of design thinking and augments it with practical tools and guides. The framework establishes a focus on shared situational perspective, and the deep understanding of both users and the AI in the empathy phase, provides a model with seven XAI levels and corresponding solution themes, and defines objective, physiological metrics for concurrent assessment of trust and workload

Evaluating experimental and theoretical measures of protein conformational dynamics

Molecular biologists have traditionally interpreted the B-factor data of a protein crystal structure as a reflection of the protein's conformational flexibility. Crystallographers, in contrast, are wary of assigning too much significance to B-factors since they can also be attributed to processes unrelated to conformational dynamics such as experimental imprecision; crystal imperfections; or rigid body motion. In this study, the usefulness of both isotropic and anisotropic B-factors as measures of conformational dynamics were evaluated using high resolution structures. Alpha-carbon B-factor values were analysed in relation to structural properties generally accepted to be correlates of conformational variability. The influence of secondary structure, amino acid type, surface exposure, distance to the centre of mass and packing density were investigated. The results support the argument that B-factors measure conformational variability by demonstrating that atoms with the highest B-factors are typically located in regions expected to have a high degree of conformational freedom. Nevertheless, the results also highlight some of the limitations of crystallographic data. Despite using high quality crystal structures, only very general qualitative trends between B-factors values and the properties investigated could be established. Thus, B-factors appear to be influenced, to a significant degree, by the numerous sources of error in a crystallographic experiment. By considering proteins with multiple published crystal structures, the existence of consensus B-factor profiles were identified. These consensus profiles were hypothesised to represent the dynamics within the crystal with a high degree of accuracy since much of the variation between individual experiments would be eliminated. However, when compared against measurements derived from molecular dynamic simulations, these consensus profiles only weakly correlated with the predictions of the computer models. Therefore, although there is some evidence to suggest that B-factors reflect conformational variability, B-factors cannot be assumed to be reliable descriptors of the internal dynamics of a protein within a crystal

Tilt-Rotor Drone

A drone is defined a an unmanned aircraft that can fly autonomously[2]. In the year 2016, there exist many applications for small scale drones. Drones, having had primarily military applications, now have use in hobby robotics, photography, and even in surveying. But drones have not yet been perfected and still have room for much improvement. Several problems with drones come in the form of battery life, stability, and size. Large drones can fit many sensors and probes, but are heavy and have less flight time. For autonomous drones, stability can be an issue even though there exist many stable drones. Finally, drones can be large which make them difficult to move around. The project proposed in this document is a form of drone called a tilt-rotor drone. It uses only two rotors, unlike the popular four rotor design. The goal is maximizing this drone\u27s flight time while minimizing its size and cost

Three-point functions of conserved supercurrents in 3D N=1\mathcal{N}=1 SCFT: general formalism for arbitrary superspins

We analyse the general structure of the three-point functions of conserved higher-spin supercurrents in 3D, $\mathcal{N}=1$ superconformal field theory. It is shown that supersymmetry imposes additional restrictions on correlation functions of conserved higher-spin currents. We develop a manifestly supersymmetric formalism to compute the three-point function $\langle \mathbf{J}^{}_{s_{1}} \mathbf{J}'_{s_{2}} \mathbf{J}''_{s_{3}} \rangle$, where $\mathbf{J}^{}_{s_{1}}$, $\mathbf{J}'_{s_{2}}$ and $\mathbf{J}''_{s_{3}}$ are conserved higher-spin supercurrents with superspins $s_{1}$, $s_{2}$ and $s_{3}$ respectively (integer or half-integer). Using a computational approach limited only by computer power, we analytically impose the constraints arising from the superfield conservation equations and symmetries under permutations of superspace points. Explicit solutions for three-point functions are presented and we provide a complete classification of the results for $s_{i} \leq 20$; the pattern is very clear, and we propose that our classification holds for arbitrary superspins. We demonstrate that Grassmann-even three-point functions are fixed up to one parity-even structure and one parity-odd structure, while Grassmann-odd three-point functions are fixed up to a single parity-even structure. The existence of the parity-odd structure in the Grassmann-even correlation functions is subject to a set of triangle inequalities in the superspins. For completeness, we also analyse the structure of three-point functions involving conserved higher-spin supercurrents and scalar superfields.Comment: 54 pages; v2: minor corrections, references added. arXiv admin note: substantial text overlap with arXiv:2210.1313